Carbonation curing in cement-based composites presents a promising and environmentally friendly solution to lower carbon emissions in the cement industry. This paper aims to provide a comprehensive review of the current research landscape encompassing this emerging technology, focusing specifically on carbonation behavior, kinetics, influential factors, and strategies to enhance carbonation degree in calcium-bearing minerals. Detailed insights into the carbonation mechanism, reactivity, and product formation of calcium silicate and calcium aluminate minerals are provided. Non-hydraulic calcium silicate minerals exhibit excellent carbonation activity while calcium aluminate minerals have minimal reactivity with CO2. Additionally, a thorough analysis of factors affecting carbonation in calcium-bearing minerals, including particle size, water-to-solid ratio, relative humidity, temperature, and CO2 concentration, is conducted. The influencing factors mentioned not only impact the carbonation rate but also influence the carbonation products as well as the carbonation degree. Special attention is paid to exploring the carbonation kinetic models based on solid-state kinetic models, and the application of the shrinking core model and surface coverage model are discussed. When applied appropriately, classical solid-state kinetic models facilitate rapid assessment of reaction kinetics and allow for optimization of carbonation conditions. Furthermore, various effective methods to improve the carbonation degree of calcium-bearing minerals are summarized, with both enhancement mechanisms and limitations of each method given. Specifically, methods that promote the dissolution of calcium ions, provide additional pathways for CO2 diffusion, or generate more nucleation sites have proven efficient for facilitating a higher carbonation degree. Finally, the paper concludes by highlighting the current challenges and limitations and providing prospects for overcoming these obstacles. •Non-hydraulic calcium silicate minerals exhibit excellent carbonation activity.•Classical solid-state kinetic models facilitate rapid assessment of reaction kinetics and allow for optimization of carbonation conditions.•Promoting the dissolution of calcium ions, facilicating the diffusion of CO2, and generating more nucleation sites are benefical for a higher carbonation degree.